Question: All of the 5th grade teachers and students from Almond went on a field trip to an art museum. Tickets were $$6.00$ each for teachers and $$4.50$ each for students, and the group paid $$55.50$ in total. A few weeks later, the same group visited a science museum where the tickets cost $$24.00$ each for teachers and $$11.50$ each for students, and the group paid $$176.50$ in total. Find the number of teachers and students on the field trips.
Explanation: Let $x$ equal the number of teachers and $y$ equal the number of students. The system of equations is: ${6x+4.5y = 55.5}$ ${24x+11.5y = 176.5}$ Solve for $x$ and $y$ using elimination. Multiply the top equation by $-4$ ${-24x-18y = -222}$ ${24x+11.5y = 176.5}$ Add the top and bottom equations together. $ -6.5y = -45.5 $ $ y = \dfrac{-45.5}{-6.5}$ ${y = 7}$ Now that you know ${y = 7}$ , plug it back into $ {6x+4.5y = 55.5}$ to find $x$ ${6x + 4.5}{(7)}{= 55.5}$ $6x+31.5 = 55.5$ $6x = 24$ $x = \dfrac{24}{6}$ ${x = 4}$ You can also plug ${y = 7}$ into $ {24x+11.5y = 176.5}$ and get the same answer for $x$ ${24x + 11.5}{(7)}{= 176.5}$ ${x = 4}$ There were $4$ teachers and $7$ students on the field trips.